QQuestionMathematics
QuestionMathematics
How do you find the central angle of a regular polygon?
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Definition of Central Angle
For a regular polygon with $$n$$ sides, we can calculate this angle using a specific formula.
The central angle of a regular polygon is the angle formed at the center of the polygon by two radii connecting to consecutive vertices.
Step 3:: Derive the Formula for Central Angle
- $$n$$ is the number of sides in the regular polygon
Where: - The result is in degrees
Step 4:: Example Calculations
- Hexagon (6 sides): $$\frac{360°}{6} = 60°
Let's demonstrate with a few examples:
Final Answer
To find the central angle of a regular polygon, divide 360° by the number of sides: \text{Central Angle} = \frac{360°}{n}.
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